Results 81 to 90 of about 6,369 (172)

Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group [PDF]

, 2013
In this paper, we investigate the sharp Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. On one hand, we apply the concentration compactness principle to prove the existence of the maximizers. While the approach here gives a different proof
Han, Xiaolong
core  

Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space

Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2421-2433, 30 January 2025.
Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space F1,∞sℝd$$ {F}_{1,\infty}^s\left({\mathbb{R}}^d\right) $$ with s≥d+1$$ s\ge d+1 $$ is clarified.
JunSeok Hwang, Hee Chul Pak
wiley   +1 more source

Prescribing integral curvature equation [PDF]

, 2015
In this paper we formulate new curvature functions on $\mathbb{S}^n$ via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even ...
Zhu, Meijun
core  

Generalized affine Hardy-Littlewood-Sobolev inequalities

We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new inequalities for log-concave functions.
Lin, Youjiang, Zhou, Jinghong, Lan, Jiaming   +2 more
openaire   +2 more sources

Effective upper bounds on the number of resonances in potential scattering

Mathematika, Volume 71, Issue 1, January 2025.
Abstract We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators −Δ+V$-\Delta +V$ with complex‐valued potentials, where d⩾3$d\geqslant 3$ is odd. The novel feature of our upper bounds is that they are effective, in the sense that they only depend on an exponentially weighted norm of V.
Jean‐Claude Cuenin
wiley   +1 more source

Regularity and Classification of Solutions to Fractional‐Order Systems With Hartree‐Type Nonlinearities

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
This paper is concerned with the positive solutions to a fractional‐order system with Hartree‐type nonlinearity and its equivalent integral system. We firstly use the regularity lifting lemma to obtain the integrability and smoothness of the solutions.
Yu-Cheng An, Guai-Qi Tian, Douglas R. Anderson   +2 more
wiley   +1 more source

Hardy, Hardy-Sobolev, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups

, 2019
In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights for such inequalities to be true.
Ruzhansky, Michael, Yessirkegenov, Nurgissa   +1 more
core  

Sharp reversed Hardy-Littlewood-Sobolev inequality with extended kernel

, 2020
In this paper, we prove the following reversed Hardy-Littlewood-Sobolev inequality with extended kernel \begin{equation*} \int_{\mathbb{R}_+^n}\int_{\partial\mathbb{R}^n_+} \frac{x_n^ }{|x-y|^{n- }}f(y)g(x) dydx\geq C_{n, , ,p}\|f\|_{L^{p}(\partial\mathbb{R}_+^n)} \|g\|_{L^{q'}(\mathbb{R}_+^n)} \end{equation*} for any nonnegative functions $f\in L^{
Dai, Wei, Hu, Yunyun, Liu, Zhao
openaire   +2 more sources

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N ≥ 3, F represents the primitive function of f, f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao, Kang-Jia Wang   +4 more
wiley   +1 more source

Critical growth elliptic problems involving Hardy-Littlewood-Sobolev critical exponent in non-contractible domains

Advances in Nonlinear Analysis, 2019
The paper is concerned with the existence and multiplicity of positive solutions of the nonhomogeneous Choquard equation over an annular type bounded domain.
Goel Divya, Sreenadh Konijeti
doaj   +1 more source